Problem: Simplify; express your answer in exponential form. Assume $x\neq 0, p\neq 0$. $\dfrac{{x^{5}p^{4}}}{{(x^{-2}p^{-5})^{-5}}}$
Answer: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${x^{5}p^{4} = x^{5}p^{4}}$ On the left, we have ${x^{5}}$ to the exponent ${1}$ . Now ${5 \times 1 = 5}$ , so ${x^{5} = x^{5}}$ Apply the ideas above to simplify the equation. $\dfrac{{x^{5}p^{4}}}{{(x^{-2}p^{-5})^{-5}}} = \dfrac{{x^{5}p^{4}}}{{x^{10}p^{25}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{5}p^{4}}}{{x^{10}p^{25}}} = \dfrac{{x^{5}}}{{x^{10}}} \cdot \dfrac{{p^{4}}}{{p^{25}}} = x^{{5} - {10}} \cdot p^{{4} - {25}} = x^{-5}p^{-21}$